1. Field of the Invention
The present invention relates to a method of calculating a minimum miscibility pressure and, more particularly, to such a method that utilizes parallel translation of coexisting equilibrium phase compositions to quickly determine the minimum miscibility pressure.
2. Setting of the Invention
For enhanced oil recovery processes involving injection of an inert gas, such as CO.sub.2 or nitrogen, miscibility with the in-place fluids in the formation can be developed through one of two multiple-contact mechanisms at pressures where first-contact phase equilibrium measurements show two-phase behavior. The two multiple-contact mechanisms are a leading edge miscibility or vaporizing mechanism, and a trailing edge miscibility or a condensing mechanism. To properly model such processes utilizing a programmable digital computer, with an equation-of-state computer program, fluid descriptions consistent with multiple-contact miscibility development are utilized. One measure of this consistency is an agreement between the minimum miscibility pressure determined from slim-tube displacements and the thermodynamic minimum miscibility pressure calculated using a programmable digital computer. Publications have previously described miscible processes using triangular compositional diagrams for the purpose of the conceptual analysis of determining the thermodynamic minimum miscibility pressure. After the minimum miscibility pressure has been determined, it is compared to laboratory results, such as the slim-tube displacements. In the equation-of-state descriptions of the fluids, usually properties of the C.sub.7 +components of the in-place oil, are adjusted to bring the descriptions into agreement. There are two common idealizations of the way in which the two-phase gas and liquid system achieves miscibility through multiple contacts. In the vaporizing mechanism, fresh or original liquid phase contacts the vapor phase whose composition is altered by repeated equilibration with the liquid. In the condensing mechanism, the composition of the liquid phase is altered by equilibration with the fresh vapor phase. The definition of thermodynamic miscibility pressure is that pressure at a fixed temperature, above which miscibility occurs for a given feed, i.e., a liquid or an oil, and the pressurizing gas solely through the multiple contact equilibrium process. The computation of this pressure is dependent upon the mechanism involved; the thermodynamic minimum miscibility pressure is assumed to be the lower of two determined bounds.
Previous methods to determine the minimum miscibility pressure have used equations of state to determine the vapor-liquid equilibrium tieline behavior combined with a strategy to locate the limiting or critical coincident tieline. A pressure is chosen for a given temperature below the thermodynamic minimum miscibility pressure. An iterative procedure is invoked to locate the coincident tieline at this pressure, usually a stepping procedure that locates to some acceptable degree of convergence the coincident tieline. The pressure is incremented upwards to locate the thermodynamic minimum miscibility pressure, taking advantage through extrapolation of the fact that the equilibrium ratio values will approach unity as the limiting coincident tieline is approached. The problem encountered in the past has been that the stepping procedure is inherently slow to approach the coincident tieline, requiring many steps. It is slowest when closest to the coincident tieline, and some judgment must be exercised by the user as to what constitutes the satisfactory location or convergence. It has become apparent to those skilled in the art that a more accurate method of determining the thermodynamic minimum miscibility pressure utilizing a programmable digital computer is needed; as well, there is a need for such a method that is more computationally efficient than those previously utilized.